Noncommutative Geometry Alain Connes

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Noncommutative GeometryAlain ConnesContentsPreface6Introduction71. Measure theory (Chapters I and V)82. Topology andK-theory (Chapter II)143. Cyclic cohomology (Chapter III)194. The quantized calculus (Chapter IV)255. The metric aspect of Noncommutative geometry34Chapter 1. Noncommutative Spaces and Measure Theory391. Heisenberg and the Noncommutative Algebra of Physical Quantities402. Statistical State of a Macroscopic System and Quantum StatisticalMechanics453. Modular Theory and the Classification of Factors484. Geometric Examples of von Neumann Algebras : Measure Theory ofNoncommutative Spaces515. The Index Theorem for Measured Foliations64Appendix A : Transverse Measures and Averaging Sequences77Appendix B : Abstract Transverse Measure Theory78Appendix C : Noncommutative Spaces and Set Theory79Chapter 2.

Introduction The correspondence between geometric spaces and commutative algebras is a familiar and basic idea of algebraic geometry. The purpose of …

  Introduction, Connes